Abstract
In this paper, we argue for a novel three-dimensionalist (3D'ist) solution to the problem of persistence, i.e. cross-temporal identity. We restrict the discussion of persistence to simple substances, which do not have other substances as their parts. The account of simple substances employed in the paper is a trope-nominalist strong nuclear theory (SNT), which develops Peter Simons' trope nominalism. Regarding the distinction between three dimensionalism (3D) and four dimensionalism (4D), we follow Michael Della Rocca's formulation, in which 3D explains persistence in virtue of same entities and 4D in virtue of distinct entities (temporal parts). SNT is a 3D'ist position because it accounts for the persistence of simple substances in virtue of diachronically identical ‘nuclear’ tropes. The nuclear tropes of a simple substance are necessary for it and mutually rigidly dependent but distinct. SNT explains qualitative change by tropes that are contingent to a simple substance. We show that it avoids the standard problems of 3D: temporal relativization of ontic predication, Bradley's regress and coincidence, fission and fusion cases. The temporal relativization is avoided because of the analysis of temporary parts that SNT gives in terms of temporal sub-location, which is atemporal part–whole relation.
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Notes
Another interesting recent attempt to explicate whole presence is by Crisp and Smith (2005). However, because their definition entails that extended simples are wholly present at each sub-region of the region of space–time they occupy (2005, 342 ff.), it fails to deal with spatio-temporally extended simples in a satisfactory fashion.
Although Jonathan Lowe (1998, 98 ff.) characterises the persistence of objects in terms of whole presence, he also introduces ‘substantial constituents approach’ in order to explain metaphysically the persistence of continuant substances (Lowe 1998, Chap. 5), which is independent of the characterisation in terms of whole presence. According to it, substances persist by virtue of the persistence of their constituent substances but substances must be eventually constituted by primitive substances which persist by just remaining identical through the time of their existence.
Cf. Kurtz (2006, 10). Sider's (2001, sec. 3.3) example of a temporal part of an endurant, i.e. a lump of clay, is a statue, which is made of exactly the same micro-particles as the lump but exists only an instant moment of lump's existence. Here, we do not take any stance on Siders' example: whether it is based on acceptable mereological assumptions or not, for instance.
Standard 4D'ists such as Sider (2001) and Hawley (2001) assume that the minimal temporal parts of objects are instantaneous and do not any have temporal extension. Hawley (2001, 28) admits, though, that there can be ‘hypothetical 4D'ists’ claiming that the minimal temporal parts are temporally extended simples. Sider agrees (2001, 60).
Let ‘≤’ be improper parthood relation between distinct entities. Trope u is strongly rigidly dependent on trope s if SRD(u, s) ≡ ¬(□ E!s) ∧ □ ((E!u → E!s) ∧ ¬(s ≤ u)) holds. Trope x of kind P is strongly generically dependent on trope y of kind R if SGD (P(x), R(y)) ≡ □ ∀x □ (Px → □ (E!x → ∃y (Ry ∧ ¬(y ≤ x)))) ∧ ◊∃x Px ∧ ¬ □ ∀x Rx holds. See Simons (1987, 294 ff.) for the more detailed discussion of these dependence relations.
In contradistinction to the SNT, Simons's (1994) Nuclear Theory does not constrain what different kinds of tropes can form a nucleus of a substance. A nucleus of substance can be constituted solely, e.g. by mass tropes, or in any case, by several tropes that belong to the same determinable kind.
A trope belongs necessarily to the determinable kind D to which it belongs. Therefore, by being strongly rigidly dependent on certain other tropes, a nuclear trope is also strongly generically dependent on the tropes that belong to determinable kinds of the tropes on which it is rigidly dependent.
Both strong rigid dependence and proper parthood are primitive formal relations, but the latter is needed in the characterization of the former.
As we will see just below, this does not yet entail that the nuclear tropes and substance i must have the same (spatial) size. However, it will be cleared up that it is not difficult to come to this conclusion.
SNT assumes that n-bundles are, as trope aggregates, identical with individuals figuring in the basic spatio-temporal relations. Similarly, c-bundles are identical with individuals. Hence, in addition to mereologically inconstant individuals (substances), tropes form mereologically constant individuals (identified with trope aggregates), i.e. c-bundles and n-bundles. For the sake of brevity, we simply speak about c-bundles and n-bundles.
Trope aggregates satisfy the thesis of strong mereological essentialism (SME) formulated by Simons (1987, 272) in modal temporal mereology.
Concrete entities (e.g. tropes) and their aggregates satisfy the principle of Expansivity formulated by Parsons (2007, 213) with respect to their spatial location: the spatial location of a whole must include the spatial locations of its proper or improper parts.
For example, Stephen Mumford (2006) has defended this claim.
Harré (1970, Chap. 11) calls simple substances ‘point centres of influence’. A point centre of influence has only dispositional features and an approximate size, which is determined by its dispositional features and the net attractive and repulsive forces between the point centre and other simple substances (i.e. point centres). In order to distinguish between simple substances and their spatial locations, we prefer to call the latter ‘centres of influence’ of simple substances. We do not assume that simple substances have point-like spatial locations.
Depending on the favoured theory of space–time, the trope bundles are either the sole relata of spatio-temporal relations (space–time relationalism) or together with space–time points (space–time substantivalism). See Sklar (1974) for further discussion of these alternative ontologies of space–time.
Note that also worm theory has to admit that a substance as a mereological sum and its temporary intrinsics share temporal sub-location without commitment to temporal relativization.
Each contingent trope u is a part of substance i at some time t: u < t i. As a consequence, both u and substance i exist at t: E! t u ∧ E! t i, cf. Simons (1987, 179). Trope u is a proper part of i at each moment of its existence: if and only if trope u exists at some time t′, u is a proper part of i at t′. However, in the SNT, the existence of a trope at t′ is explained in terms of temporal location. Thus, u is a temporary part of i because the temporal location of the corresponding c-bundle is a part of the temporal location of i.
Grounded internal relations are relational features of entities determined by the properties and/or relations instantiated by the same or distinct entities (e.g. the proper parts of the first entities). Cf. Keinänen (2005, Sec. 3.3.4) for a more comprehensive account of the different kinds of grounded internal relations.
What Bradley's original problem exactly is a difficult interpretative question. There is no room in this paper to address that problem. Therefore, it is not reasonable to consider Bradley's original regress here. For a historical discussion of it, see Candlish and Basile (2009, Chap. 6).
The relata of relational tropes must not be strongly rigidly dependent on each other. This is necessary because otherwise, a contingent trope SRD on two nuclear tropes, which are SRD on each other, would be a relational trope, cf. Keinänen (2005, Sec. 4.3.9).
Here, we allude to Parfit's problem of dividing personality and the traditional problem of the Ship of Theseus, for example. For a brief exposition of these problems, see Sider (2001, 143–147). In the fission and fusion cases, entities divide or fuse, and the question is how to determinate identity relations in these scenarios.
References
Armstrong, D. M. (1997) A World of States of Affairs. Cambridge University Press, Cambridge.
Bradley, F. H. (1893). Appearance and Reality. Oxford University Press, Oxford.
Campbell, K.K. (1990). Abstract Particulars. Basil Blackwell, Oxford.
Candlish, S. & Basile, P. (2009). Francis Herbert Bradley. In: Zalta, E.N. (Ed.) The Stanford Encyclopedia of Philosophy. Spring 2009 Edition. Available from http://plato.stanford.edu/archives/spr2009/entries/bradley/.
Crisp, T.M. & Smith, D.P. (2005). ‘Wholly present’ defined. Philosophy and the Phenomenological Research 71(2): 318-344.
Della Rocca, M. (2009). Primitive Persistence and the Impasse between Three-Dimensionalism and Four-Dimensionalism, Journal of Philosophy (in press).
Denkel, A. (1996). Object and Property. Cambridge University Press, Cambridge.
Denkel, A. (1997). On the Compresence of Tropes. Philosophy and Phenomenological Research LVII(3): 599-606.
Harré, R. (1970). The Principles of Scientific Thinking. Macmillan, London.
Haslanger, S. (1989). Endurance and Tempory Intrinsics. Analysis 49: 119-125.
Hawley, K. (2001). How Do Things Persist. Oxford University Press, Oxford.
Hawthorne, J. (2008). Three-Dimensionalism vs. Four-Dimensionalism. In: Sider, T., Hawthorne, J. & Zimmerman, D. (Eds.) Contemporary Debates in Metaphysics (pp. 263-282). Oxford University Press, Oxford.
Keinänen, M (2005). Trope Theories and the problem of Universals. Philosophical Studies from the University of Helsinki, Helsinki.
Kurtz, R.M. (2006). Introduction to Persistence: What's the Problem? In: Haslanger, S. & Kurtz, R.M. (Eds.) Persistence – Contemporary Readings (pp. 1-26). MIT Press, Cambridge.
Lewis, D.K. (1986). On The Plurality of the Worlds. Basil Blackwell, Oxford.
Lowe, E.J. (1998). The Possibility of Metaphysics - Substance, Identity and Time. Clarendon Press, Oxford.
Maurin, A-S. (2002). If Tropes. Kluwer Academic Publishers, Dordrecht.
Maurin, A-S. (2009). Trope Theory and the Bradley's Regress. Synthese (in press).
Mellor, D.H. (1981). Real Time. Cambridge University Press, Cambridge.
Mumford, S. (2006). The Ungrounded Argument. Synthese 149: 471-489.
Parsons, J. (2007). Theories of Location, In: Zimmerman, D. (Ed.) Oxford Studies in Metaphysics vol. 3 (pp. 201-232). Oxford University Press, Oxford.
Sider, T. (2001). Four Dimensionalism - An Ontology of Persistence and Time. Oxford University Press, Oxford.
Simons, P.M. (1987). Parts - a Study in Ontology. Clarendon Press, Oxford.
Simons, P.M. (1994). Particulars in Particular Clothing - Three Trope Theories of Substance. Philosophy and Phenomenological Research LIV(3): 553-575.
Simons, P.M. (2003). Tropes, Relational. Conceptus 35: 53-73.
Simons, P.M. (2004). Extended Simples: A Third Way Between Atoms and Gunk. Monist 87: 371-384.
Sklar, L. (1974). Space, Time, and Spacetime. University of California Press, London.
Van Inwagen, P. (1990). Four-dimensional Objects. Nous 24: 245-255.
Williams, D. C. (1953a). On the Elements of Being I. Review of Metaphysics 7: 3-18.
Williams, D. C. (1953b). On the Elements of Being II. Review of Metaphysics 7: 171-192.
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Keinänen, M., Hakkarainen, J. Persistence of Simple Substances. Int Ontology Metaphysics 11, 119–135 (2010). https://doi.org/10.1007/s12133-010-0063-1
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DOI: https://doi.org/10.1007/s12133-010-0063-1